Engaging Young Children in Mathematics

Standards for Early Childhood Mathematics Education

Douglas H. Clements, Julie Sarama, Associate Edito DiBiase, Ann-Marie DiBiase

• Publisher: Routledge
• Year: 2003
• ISBN:
  9781135635336
• Edition: 1
• Topic: Education
• Subtopic: Education General

This book consists of conclusions drawn from the expertise shared at the Conference on Standards for Prekindergarten and Kindergarten Mathematics Education. It offers substantive detail regarding young students' understandings of mathematical ideas.

I
Major Themes and Recommendations

Summary of Part I: Assumptions and Recommendations

This section summarizes the two assumptions and the 16 recommendations that are described in detail in chapter 1, which comprises Part I.

Assumption 1: Knowledge of what young children can do and learn, as well as specific learning goals, are necessary for teachers to realize any vision of high-quality early childhood education, (p. 26)

Assumption 2: Prekindergarten children have the interest and ability to engage in significant mathematical thinking and learning, (p. 28)

Recommendation 1: Equity is a major concern in mathematics education at all levels. There is an early developmental basis for later achievement differences in mathematics: Children from different sociocultural backgrounds may have different foundational experiences. Programs need to recognize sociocultural and individual differences in what children know and in what they bring to the educational situation. Knowledge of what children bring should inform planning for programs and instruction, (p. 29)

Recommendation 2: The most important standards for early childhood are standards for programs, for teaching, and for assessment. These should be built on flexible, developmental guidelines for young children?s mathematical learning. Guidelines should be based on available research and expert practice, focus on and elaborate the big ideas of mathematics, and represent a range of expectations for child outcomes that are developmentally appropriate, (p. 31)

Recommendation 3: Mathematics for young children should be an integrated whole. Connections?between topics, between mathematics and other subjects, and between mathematics and everyday life?should permeate children?s mathematical experiences, (p. 73)

Recommendation 4: As important as mathematical content are general mathematical processes such as problem solving, reasoning and proof, communication, connections, and representation; specific mathematical processes such as organizing information, patterning, and composing; and habits of mind such as curiosity, imagination, inventiveness, persistence, willingness to experiment, and sensitivity to patterns. All should be involved in a high-quality early childhood mathematics program, (p. 73)

Recommendation 5: Curriculum development and teaching should be informed by research on teaching and learning and by the wisdom of expert practice. Educators and policymakers should support and insist on approaches to teaching, learning, curriculum, and assessment that are developed and tested extensively with children, (p. 74)

Recommendation 6: Mathematical experiences for very young children should build largely upon their play and the natural relationships between learning and life in their daily activities, interests, and questions, (p. 75)

Recommendation 7: Teachers? most important role with respect to mathematics should be finding frequent opportunities to help children reflect on and extend the mathematics that arises in their everyday activities, conversations, and play, as well as structuring environments that support such activities. Teachers should be proactive as well in introducing mathematical concepts, methods, and vocabulary, (p. 75)

Recommendation 8: Teachers should purposefully use a variety of teaching strategies to promote children?s learning. Children benefit from a thoughtful combination of carefully planned sequences of activities and of integrated approaches that occur throughout the day. Successful early childhood teachers build on children?s informal knowledge and everyday activities, considering children?s cultural background, language, and mathematical ideas and strategies, (p. 76)

Recommendation 9: Children should benefit from the thoughtful, appropriate, ongoing use of various types of technology. Especially useful are computer tools that enrich and extend mathematical experiences, (p. 76)

Recommendation 10: Teachers should endeavor to understand each child?s own mathematical ideas and strategies. Teachers should use those understandings to plan and adapt instruction and curriculum, (p. 77)

Recommendation 11: Teachers should help children develop strong relationships between concepts and skills. Skill development is promoted by a strong conceptual foundation, (p. 77)

Recommendation 12: Interview and performance tasks and ongoing, observational forms of assessment are useful and informative ways of assessing young children?s mathematical learning and should be integrated as appropriate into the early childhood mathematics curriculum. The primary goal of assessing young children should be to understand children?s thinking and to inform ongoing teaching efforts, (p. 79)

Recommendation 13: Professional development should be based on research and expert practice. It requires multiple strategies and an understanding of the variety of professional development models, with special emphasis on the importance of teacher leaders and collegial support groups. It needs to be sustained and coherent, (p. 82)

Recommendation 14: Deep knowledge of the mathematics to be taught, together with knowledge of how children think and develop those skills and understandings, is critical for improving teaching and should be learned in preservice and professional development programs, (p. 83)

Recommendation 15: One effective way to promote professional development is through the use of high-quality curriculum materials and programs. These should be included in professional development programs. (p. 83)

Recommendation 16: A coordinated effort should be created to translate the information in this book into a variety of forms for different audiences, (p. 85)

Recommendation 17: State agencies should collaborate across all states to form more coherent and related state mandates and guidelines for mathematics for young learners. Governments should provide adequate funding and structures so as to provide high-quality early childhood education for all children, including high-quality professional development for the adults who care for them. (p. 85)

1
Major Themes and Recommendations

Douglas H.Clements
University at Buffalo, State University of New York

The Conference on Standards for Prekindergarten and Kindergarten Mathematics Education was held to facilitate early communication between, and coordination of efforts by, the educational leaders and agencies who are developing mathematics standards and curricula for young children. An 18-person working group, representative of conference participants, met in a follow-up meeting to summarize the main points raised, and research presented, at the conference, as well as the recommendations for action.¹This group synthesized the various resources compiled by the conference participants (including transcriptions from each of the working groups and plenary sessions of the conference). The first draft was circulated widely among representatives of the more than 100 participants of the initial Conference and several additional experts; their advice was considered in producing the final revision of this chapter. Thus, these Major Themes and Recommendations represent, to the best of our ability, the contributions of existing research theory and the collaborative thinking of representatives from the diverse fields concerned with early mathematics education.

The five major themes are as follows:

• Standards in Early Childhood Education
• Mathematics Standards and Guidelines
• Curriculum, Learning, Teaching, and Assessment
• Professional Development
• Toward the Future: Implementation and Policy

STANDARDS IN EARLY EDUCATION

Should there be standards for early childhood mathematics education? Should the nature of these standards change for children of different ages? This section summarizes themes on general policy and pedagogical issues related to the creation and use of standards for young children.

All individuals concerned with educational standards must conscientiously distinguish two types of standards. One type prescribes standards as requirements for mastery. The second type promotes standards as a vision of excellence.² An example of the former is the use of standards in making high-stakes decisions such as retaining students in a grade or determining teachers” salaries. An example of the latter is the vision of mathematics education in the Principles and Standards for School Mathematics (PSSM; National Council of Teachers of Mathematics [NCTM], 2000). Few specific mastery requirements are provided in that document. That is the basis for criticism by some. However, the NCTM has always taken the position that its mission was to establish a vision, not to dictate details. We agree with that position for the NCTM Standards, but also believe that certain specifics must be provided as the next step. Indeed, one rationale for the collaborative work of the Conference was to provide additional specific information, for example, what to look for in a program, in children's learning, and in teacher and caregiver³ preparation.

There is a substantial and critical difference between standards as a vision of excellence and standards as narrow and rigid requirements for mastery. Only the former, including fexible guidelines and ways to achieve learning goals, is appropriate for early childhood mathematics education at the national level.

One aim of this book is to provide such specific yet flexible guidelines and ways to achieve goals for early childhood mathematics education. This book defines standards as guidelines that help realize visions of high-quality mathematics education. Standards can be for program and teachers, for children, or for both. At the Conference, there was broad consensus that standards for programs and teachers were essential. Such standards protect children from harm and contribute to their development and learning.

In contrast, early childhood educators historically have been resistant to specifying learning goals for very young children (Bredekamp,chap. 2, this volume). A major concern from both a philosophical and pedagogical perspective is that, because children develop and learn at individually different rates, no one set of age-related goals can be applied to all children. A specific learning time line may create inaccurate judgments and categorizations of individual children, limit the curriculum to those outcomes and lead to inappropriate teaching of narrowly defined skills, and limit the development of the “whole child” (Bredekamp,chap. 2, this volume).

In defining and implementing standards, we seek to avoid these abuses and realizing the advantages of specifying goals. First, such standards can demystify what children are able to do, by describing their mathematical thinking and capabilities at various age levels. Second, they can provide teachers of young children with needed guidance about appropriate expectations for children's learning and can focus that learning on important knowledge and skills, including critical-thinking skills. Third, standards can help parents better understand their children's development and learning and provide appropriate experiences for them.

Fourth, in the classroom and home, such goals can help “level the playing field,” achieving equity by ensuring that the mathematical potential of all young children is developed throughout their lives. Teachers have welcomed more specific guidance on learning goals linked to age/grade levels, as those published a recent joint position statement on developmentally appropriate practices in early literacy (Bredekamp,chap. 2, this volume; National Association for the Education of Young Children and the International Reading Association, 1998). Providing guidance is even more crucial for mathematics, where teachers” own knowledge of the discipline is typically insufficient to make these judgments (Bredekamp,chap. 2, this volume).

Fundamental questions for teachers are what to teach, when to teach it, and how to teach it meaningfully. For goals to truly be useful guides, they need to be more closely connected to age/grade levels than are those in NCTM's visionary PSSM. This assertion, voiced by Bredekamp and others, was echoed by most participants throughout the Conference. In summary, high-quality standards can provide a foundation upon which to build a program that is coherent with the K-l 2 system students will enter. We can assume the following:

Assumption 1: Knowledge of what young children can do and learn, as well as specifc learning goals, are necessary for teachers to realize any vision of high-quality early childhood education.

Admittedly, pressure to create standards also comes from the concern that if experts do not do so, someone with far less experience will (Lindquist & Joyner,chap. 20, this volume). However, we...

Table of contents

• Cover
• Half Title
• Studies in Mathematical Thinking and Learning
• Full Title
• Copyright
• Contents
• Preface
• PART I: MAJOR THEMES AND RECOMMENDATIONS
• PART II: ELABORATION OF MAJOR THEMES AND RECOMMENDATIONS
• Author Index
• Subject Index